Corwin, IvanLiu, ZhipengWang, Dong2017-12-072017-12-072015-08-13Corwin, Ivan; Liu, Zhipeng; Wang, Dong. Fluctuations of TASEP and LPP with general initial data. Ann. Appl. Probab. 26 (2016), no. 4, 2030--2082. doi:10.1214/15-AAP1139.https://hdl.handle.net/1808/25603We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar-Parisi-Zhang universality classTASEPLast passage percolationKardar–Parisi–ZhangArticle10.1214/15-AAP1139openAccess